Problem: Simplify the following expression: $ q = \dfrac{9r - 9}{r + 10} - \dfrac{-1}{6} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{9r - 9}{r + 10} \times \dfrac{6}{6} = \dfrac{54r - 54}{6r + 60} $ Multiply the second expression by $\dfrac{r + 10}{r + 10}$ $ \dfrac{-1}{6} \times \dfrac{r + 10}{r + 10} = \dfrac{-r - 10}{6r + 60} $ Therefore $ q = \dfrac{54r - 54}{6r + 60} - \dfrac{-r - 10}{6r + 60} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{54r - 54 - (-r - 10) }{6r + 60} $ Distribute the negative sign: $q = \dfrac{54r - 54 + r + 10}{6r + 60}$ $q = \dfrac{55r - 44}{6r + 60}$